incumbency as a source of spillover effects in mixed ...jhainm/paper/hk2008contamination.pdf ·...

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Electoral Studies xx (2008) 1e15www.elsevier.com/locate/electstud

Incumbency as a source of spillover effects in mixed electoralsystems: Evidence from a regression-discontinuity design*

Jens Hainmueller a, Holger Lutz Kern b,�a Harvard University, Department of Government, USAb Cornell University, Department of Government, USA

Abstract

In this paper we demonstrate empirically that incumbency is a source of spillover effects in Germany’s mixed electoral system.Using a quasi-experimental research design that allows for causal inferences under a weaker set of assumptions than the regressionmodels commonly used in the electoral systems literature, we find that incumbency causes a gain of 1.4e1.7 percentage points inPR vote shares. We also present simulations of Bundestag seat distributions to show that spillover effects caused by incumbency aresufficiently large to trigger significant shifts in parliamentary majorities.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Incumbency; Mixed electoral systems; Contamination; Causal inference; Regression-discontinuity design

1. Introduction

Since the early 1990s, more than 30 countries haveadopted mixed electoral systems that combine single-member districts (SMD) in one tier with proportionalrepresentation (PR) in a second tier. Once regardedas an oddity among the ideal types of proportionaland Westminster-type (first-past-the-post) electoralsystems, mixed systems have begun to attract seriousscholarly attention (Gschwend, 2006; Massicotte andBlais, 1999; Shugart and Wattenberg, 2001; Ferrara

* This is one of several joint papers by the authors; the ordering of

names reflects a principle of rotation. Both authors contributed

equally to this paper. We thank Barry Burden, Alexis Diamond,

Dominik Hangartner, Walter R. Mebane, Jr., the reviewers, and the

editor for comments. The usual disclaimer applies.� Corresponding author.

E-mail addresses: [email protected] (J. Hainmueller),

[email protected] (H.L. Kern).

0261-3794/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.electstud.2007.10.006

Please cite this article in press as: Hainmueller, J., Holger Lutz Kern, Incu

Evidence from a regression-discontinuity design, Electoral Stud. (2008), d

et al., 2005). Recent work investigates how such sys-tems arise (Bawn, 1993; Shugart, 2001), affect incen-tives for strategic voting and entry (Bawn, 1999;Gschwend, 2006; Gschwend et al., 2003; Moser andScheiner, 2005), influence the behavior of legislators(Lancaster and Patterson, 1990; Stratmann and Baur,2002; Bawn and Thies, 2003), and shape national partysystems (Shugart and Wattenberg, 2001; Ferrara et al.,2005).

One reason for the increased attention devoted tomixed electoral systems is the apparent opportunitythey offer for ‘‘a controlled comparison of votingpatterns under different electoral rules’’ (Moser andScheiner, 2005: 260). Mixed electoral systems seem-ingly allow scholars to use the outcomes generated inthe SMD and PR tiers to compare the effects of differ-ent types of electoral rules while at the same time hold-ing constant confounding variables (Lancaster andPatterson, 1990; Bawn, 1993; Stratmann and Baur,

mbency as a source of spillover effects in mixed electoral systems:

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2 J. Hainmueller, H.L. Kern / Electoral Studies xx (2008) 1e15

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2002; Moser, 1999; Moser and Scheiner, 2005). Yet asFerrara et al. (2005) point out, this line of reasoning isonly correct to the extent that the two tiers are truly in-dependent from each other; the operation of each tiermust be unaffected by the presence of a second tiercharacterized by a different set of electoral rules.Recent empirical evidence for the existence of ‘‘con-tamination’’ or spillover effects between the two tiersin mixed electoral systems (Herron and Nishikawa,2001; Cox and Schoppa, 2002; Ferrara et al., 2005)makes this a doubtful assumption.

Our paper builds on this literature by identifying in-cumbency as another source of spillover. Prior researchhas examined spillover effects on PR vote shares causedby the mere presence of district candidates. But anextensive literature in American politics (and to a lesserextent comparative politics) has demonstrated thatincumbency status has a significant impact on districtvote shares. Relating this well-established fact to thespillover literature leads us to our main theoretical argu-ment: if the mere presence of a district candidate hasa positive effect on her party’s PR vote share in herdistrict, it seems plausible to expect incumbency tohave an even bigger effect. After all, winning a districtgives a party and its incumbent legislator 4 years to con-vince voters of their merits, a much longer time spanthan the relatively brief election campaigns highlightedas the source of spillover by the existing literature. Thus,incumbent legislators should not only enjoy an electoraladvantage in terms of SMD votes, but also be able toattract additional PR votes in their districts.

We test this prediction against data from Germanfederal elections, using a quasi-experimental regres-sion-discontinuity (RD) design to estimate the causaleffects of incumbency.1 The RD design allows forcausal inferences under a weaker set of assumptionsthan the regression models commonly used in theelectoral systems literature. We find that incumbencycauses a gain of about 1.4e1.7 percentage points inPR vote shares, a result that is robust to the use of dif-ferent measures of incumbency. We also find that mostof the votes that incumbents are able to attract for their

1 In Germany’s ‘‘mixed-member-proportional’’ system (Shugart

and Wattenberg, 2001), voters cast two ballots, one for district can-

didates and one for party lists. Seat allocation is compensatory; a par-

ty’s total number of seats in the Bundestag is proportional to its list

vote share (conditional on reaching a 5% threshold or winning at

least three district seats). Seats won in the plurality-rule SMDs are

subtracted from the total number of seats allocated to each party ac-

cording to its PR vote share in each state. For overviews of Germa-

ny’s electoral and party system see Falter et al. (2000) and von

Alemann (2003).



parties come from the other major party. To the best ofour knowledge, our paper is also the first to analyze thesubstantive impact of spillover on the distribution oflegislative seats. Our simulations show that spillovercaused by incumbency leads to net shifts of 10e15legislative seats and is thus sufficiently large to poten-tially trigger decisive shifts in Bundestag majorities.

The paper is structured as follows. In Section 2, wereview prior work on spillover effects. Section 3 spellsout our theoretical argument. Sections 4 and 5 discussthe statistical model and the data. In Section 6, wepresent the results. Section 7 concludes.

2. Spillover effects

Spillover effects can operate in two directions.2

First, the presence of single-member districts couldaffect the electoral competition in the PR tier. Basedon Germany’s experience with a mixed electoralsystem, Duverger (1986: 72), for example, arguesthat the two-party competition typical of SMDs spillsover to the PR tier, leading to overall ‘‘pressure towarda two-party system’’ despite the existence of a morepermissive proportional tier.

Second, the direction of causality also could be thereverse, from the proportional tier to single-memberdistricts. Cox and Schoppa (2002: 1031) note thatthe Duvergerian tendency toward two-party competi-tion in SMDs (Duverger, 1954; Cox, 1997) appearsto be muted in the SMD tier of Germany’s, Japan’s,and Italy’s mixed systems. They attribute this fact tosmall parties’ incentives to run district candidates inmany districts, even if they have no chance of win-ning, ‘‘in order to give their party a human face thatthey can use to boost the party’s [PR] vote totals.’’Herron and Nishikawa (2001) find that in Russiaand Japan the number of parties in the SMD tier islarger than in ‘‘pure’’ SMD systems. They too attri-bute this finding to the strategy pursued by smallparties to run district candidates, even hopeless ones,in as many districts as possible in order to increasevoter awareness of their programs and vote shares inthe PR tier. Ferrara et al. (2005: chapter 3) presentsimilar results for a larger number of mixed electoral

2 We adopt Ferrara et al.’s (2005: 8e9) definition of spillover

(which they call contamination): ‘‘Contamination is present, at the

micro-level, when the behavior of a voter, a party, a candidate, or

a legislator in one tier of the election is demonstrably affected by

the institutional rules employed in the other tier. At the aggregate

level, contamination is observed when a particular outcome produced

in one tier (like the number of parties) is affected by the institutional

features of the other tier.’’


oi:10.1016/j.electstud.2007.10.006

3 Cox and Schoppa (2002) therefore only present estimates for Jap-

anese elections, and Ferrara et al. (2005) restrict their discussion of

Germany to the 1953 Bundestag election, noting that in later elec-

tions even small parties such as the Liberals (FDP) or Greens ran can-

didates in virtually every district.

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systems, showing that parties’ PR vote shares arepositively associated with the presence of districtcandidates.

While these results are quite intriguing, theirinterpretation remains ambiguous. Parties might placecandidates in districts in which they expect to bemore popular than average or where they have the or-ganizational resources to run a campaign. If this werethe case, the positive association between the presenceof district candidates and PR vote shares would be (atleast partially) spurious. Of course, scholars workingon spillover effects are aware of the possibility ofsuch selection effects and attempt to address them byadding control variables to their models. Cox andSchoppa (2002: 1034), for example, use past voteshares as a measure of party popularity in each district.Herron and Nishikawa (2001) add a dummy variablefor incumbency as a proxy for popularity, and for theJapanese case also include past vote shares from upperhouse elections for some parties. For some countries,Ferrara et al. (2005) add incumbency as a proxy forpopularity in addition to demographic or regionalcontrols.

However, given the limited set of control variablesavailable to these authors, it seems likely that thereremains a fair amount of selection bias due to theexistence of unobserved confounders, i.e., variablesthat are correlated with both the independent variablesand the dependent variable. For example, a party’sexpectation to do particularly well in a district mightincrease the probability that it runs a candidate inthis district. If parties’ expectations are also correlatedwith final vote shares, which seems rather likely, thiswould induce omitted variable bias. In order to yieldunbiased causal estimates, previously used modelshad to make the assumption that treatment assignmentis unconfounded conditional on the included controlvariables (Rubin, 1974; Rosenbaum, 2002). Thisimplies that for each party, conditional on past voteshares or some other regional or demographic controlvariable, the probability of running a district candidateis the same in districts in which a candidate actuallyruns or does not run. This seems to be an overly restric-tive assumption. As we will show below, the RD designin contrast helps us to avoid any selection bias fromunobserved confounders.

There exists another equally thorny problem.Estimating spillover effects caused by the presence ofdistrict candidates is only possible if parties runcandidates in some but not all districts. In manycountries, however, most small parties regularly runcandidates in all or almost all districts. Some scholars



have argued that this provides strong evidence thatparties are aware of the existence of spillover effectsand take advantage of it (Cox and Schoppa, 2002).However, the identification of treatment effects be-comes impossible without variation in the treatmentvariable.3 Since incumbency varies both acrossdistricts and over time, this does not pose a problemfor us. We can estimate spillover effects even for Bun-destag elections in which small parties ran candidatesin every district.

3. Incumbency advantage and spillover

Why do we predict incumbency to have an effect onPR vote shares? A large body of work in Americanpolitics (and to a much lesser extent comparativepolitics) has examined the advantages that incumbentlegislators enjoy when running in the next election.The causes of incumbency advantage identified inthis literature include redistricting, strategic entry andexit, the increased visibility and name recognition ofincumbents, and electoral payoffs from securingpork-barrel projects for their districts and helpingconstituents deal with the bureaucracy (Cox andKatz, 2002; Ansolabehere et al., 2000; Ansolabehereand Snyder, 2004; Levitt and Wolfram, 1997; Kingand Gelman, 1991; Cain et al., 1984; Gaines, 1998).

With rare exceptions (Bawn, 1999; Moser andScheiner, 2005), explanations of SMD voting behaviorin Germany have stressed national factors such asparliamentary coalitions or party platforms whiledownplaying district and candidate characteristics(Jesse, 1988; Porter, 1995). According to Pappi andMnich (1992), Jesse (1988), and Cox (1997: 160),ticket-splitting voters will generally cast their twoballots for the parliamentary coalition they hope tosee elected. Smaller parties such as the Liberals orthe Greens cannot form a parliamentary coalitionwith one of the major parties unless they reach the5% threshold set by election law. Since parties alwaysmake their coalition preferences known well before theelection, CDU voters, for example, might thereforechoose to cast their first votes for the CDU but theirsecond votes for the Liberals.

With one exception (Lancaster, 1998), the questionof whether candidate characteristics have an


oi:10.1016/j.electstud.2007.10.006

4 Strictly speaking, party incumbency only subsumes legislator in-

cumbency if incumbent legislators do not switch parties. We ignore

this complication here since party switches are extremely rare in

Germany.

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independent effect on PR vote shares has not been raisedin the literature on voting behavior in Germany. That weshould not simply discount this possibility is evidentfrom the spillover effects literature, which has consis-tently found that the presence of district candidates ispositively associated with PR vote shares (Cox andSchoppa, 2002; Herron and Nishikawa, 2001; Ferraraet al., 2005). However, if the mere presence of a districtcandidate is sufficient to boost her party’s PR vote share,it seems quite plausible to expect candidate characteris-tics such as incumbent status to have an even biggereffect. After all, winning a district gives a party andits incumbent legislator 4 years to convince voters oftheir merits, a much longer time span than the relativelybrief election campaigns that the existing literature onspillover effects stresses as a source of spillover. Wetherefore predict that incumbent legislators do notonly enjoy an electoral advantage in terms of SMDvotes, as previously shown by Bawn (1999) and Moserand Scheiner (2005), but that they are also able to attractadditional PR votes for their parties.

Which causal mechanisms might lead incumbencyto affect PR vote shares? We know from surveys ofmembers of the Bundestag that they spend a significantamount of time in their districts, helping their constit-uents deal with local, state, and federal bureaucracies,securing pork-barrel projects, and maintaining closecontacts to their local party organizations and constit-uents (Herzog et al., 1990; Patzelt, 1993; Lancasterand Patterson, 1990). Many legislators themselves con-sider ombudsman-type services and success in securingpork as important determinants of their re-electionprospects (Lancaster and Patterson, 1990; Patzelt,1993; Porter, 1995). Stratmann and Baur (2002) findthat legislators who enter the Bundestag through theSMD tier instead of party lists systematically seekout committee assignments that help them better repre-sent the interests of their districts. A recent study byKlingemann and Wessels (2001) shows that voters’perception of the performance of their district repre-sentative was strongly associated with SMD votechoice in the 1998 Bundestag election. If voters rewardincumbents for good district service, which seemslikely, it might also be possible for popular incumbentsto attract additional PR votes for their parties.

A related body of evidence suggests that parties dotake district service into account when nominatingdistrict candidates, and that incumbents who fail torepresent the interests of their districts are sometimesdenied renomination (Zeuner, 1970: 144e146; Patzelt,1993: 366e382; Porter, 1995: 77e105). If the perfor-mance of incumbents has an effect on parties’ PR



votes, it is of course not very surprising to see partiestake a strong interest in the quality of the districtservice provided by their incumbent legislators.

Unfortunately, time-series data on district serviceare not available and we will have to leave an investi-gation of this potential causal mechanism to futurework. One causal mechanism that we can examine,however, is challenger quality (Cox and Katz, 2002;Jacobson, 1987). To test whether any effect that incum-bency might have on SMD and PR vote shares is due toincumbents’ ability to deter high-quality opponents,we will perform separate estimations for sub-samplesof districts in which the other major party did notrun a ‘‘shadow’’ incumbent. Shadow incumbents aremembers of the legislature elected through party lists.Since many of them run in district races, many districtsactually see two or more Bundestag members runagainst each other, only one of them being the districtincumbent. The presence of such shadow incumbentsthus gives us an excellent measure of candidate quality.Shadow incumbents, after all, already made it into theBundestag. It would be hard to imagine moreexperienced and formidable challengers.

3.1. Measures of incumbency

We rely on two distinct measures of incumbency:legislator incumbency and party incumbency. Follow-ing Gelman and King (1990), the legislator incum-bency advantage is defined as the difference betweenthe district vote share received by an incumbent legis-lator in her district and the district vote share receivedby the incumbent party in that district, if the incumbentlegislator does not run. Following Lee (2008), party in-cumbency advantage in contrast measures the electoraladvantage to being the incumbent party in a district,relative to not being the incumbent party. Party incum-bency thus subsumes legislator incumbency, but incontrast to legislator incumbency, it is not conditionalon the incumbent legislator running.4

There are two reasons, one theoretical and the othermethodological, for why we employ two differentdefinitions of incumbency. Our theoretical expectationis that spillover effects arise primarily from incumbentlegislators’ success in representing the interests of theirconstituents. This suggests that legislator incumbency isthe appropriate measure of incumbency. However, if


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a popular incumbent’s reputation ‘‘rubs off’’ on the nextcandidate her party puts forward after she decides to re-tire (especially if she explicitly endorses the candidate),a focus on legislator incumbency would lead us to un-derestimate the size of spillover effects. Since we are in-terested in estimating the overall magnitude of spillover,this suggests that party incumbency might be a more ap-propriate measure. Moreover, from a methodologicalperspective, party incumbency is the preferred measure,since estimates of the causal effects of legislator incum-bency are potentially biased due to strategic exit. If in-cumbent legislators choose not to run when theprospects for winning their districts are poor, estimatesof legislator incumbency advantage will be biased (Gel-man and King, 1990; Jacobson and Dimock, 1994). Thisis probably not a serious concern in German electionssince most district incumbents also run on party listsand therefore have a good chance of retaining their leg-islative seats even if they lose their district race. Tables 1and 2 present empirical evidence that also suggests thatstrategic exit is an unlikely source of bias. As we can seein Table 1, about 80% of incumbent legislators run. Themedian age of running incumbents is 52 years, whereasretiring incumbents are almost a full decade older. Thisis consistent with the notion that incumbents’ decisionto retire is not primarily strategic in nature. Table 2reports marginal effect coefficients (partial derivatives)of simple probit response functions of incumbents’decision to run on age and closeness of the election.As one would expect, age has a negative, statisticallysignificant effect on the probability of running.Margins of victory in the last as well as the upcomingelection (which measure the closeness of the last raceand serve as a proxy for the perceived closeness of theupcoming race) are generally statistically insignificantand have the wrong sign in three out of four models.

Table 1

Incumbents that run or exit

Election

year

% Of incumbents

that run

Median age

of incumbents

that run

Median age

of incumbents

that exit

All CDU SPD All CDU SPD All CDU SPD

1961 79 80 72 55 56 54 62 62 61

1969 69 68 69 50 50 48 63 63 63

1972 70 68 72 48 49 48 62 62 61

1983 88 90 87 50 50 49 53 53 54

1987 83 87 71 53 53 52 58 57 60

1990 75 73 80 52 52 52 61 61 61

1994 77 77 78 53 53 53 62 63 60

1998 79 80 76 55 55 55 59 59 59

Average 77 78 76 52 53 51 61 61 60



Their inclusion adds virtually nothing to the predictivepower of the models. These results suggest that strategicexit is not an important feature of German federal elec-tions. Still, we will present estimates for the causal ef-fects of legislator as well as party incumbency to dealwith this potential source of bias.

4. Regression-discontinuity designs

We rely on an RD design to obtain estimates of thecausal effects of party and legislator incumbency. TheRD design is a quasi-experimental technique that al-lows for the identification of treatment effects insettings in which assignment to treatment changesdiscontinuously as a function of one or more underlyingvariables. Its key advantage over conventionalregression models is that it is not sensitive to omittedvariables; it mimics a randomized experiment in this re-spect. Since the RD design has rarely been used in thepolitical science literature we explain it here in detail.

The earliest published use of an RD design dates backto Thistlethwaite and Campbell (1960). In their seminalwork, they examine the effect of scholarships on careeroutcomes by comparing students just above and belowa threshold in test scores that determines whether stu-dents receive an award or not. The underlying idea isthat in the close neighborhood of the threshold, assign-ment to treatment is ‘‘as good as random.’’ Unlucky stu-dents who just miss the threshold are assumed to bevirtually identical to lucky ones who score just abovethe cutoff value. The only difference between them isthat the latter receive the scholarship while the formerdo not, thus providing Thistlethwaite and Campbellwith a suitable counterfactual for causal inference.

Whenever the data-generating process is character-ized by a treatment assignment mechanism that issolely based on exceeding a threshold on a predeter-mined covariate, a randomized experiment is ‘‘hiding’’in the data. In a sense, the RD design allows us to sep-arate this experiment from the rest of the data, which istainted by selection effects. Such situations arise sur-prisingly often in empirical settings. Since the earlywork by Thistlethwaite and Campbell, RD designshave been frequently used in various disciplines suchas medicine and public health, education, economics,and sociology (Shadish et al., 2002 provide a review).Recent work in econometrics and program evaluationalso demonstrates a growing interest in their use.Most relevant for the purpose of this paper, economistDavid Lee (2008) has for the first time applied the RDdesign to the study of electoral behavior. Butler andButler (2007) use it to study split-party delegations in


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Table 2

Incumbents’ age and the probability of exit

CDU SPD

DV: Running (1 if running, 0 otherwise)

Mean: 0.78 0.76

SD: 0.02 0.02

1 2 3 4

Age �0.018 (0.001) �0.017 (0.001) �0.020 (0.002) �0.020 (0.002)

Margin of victory 0.004 (0.002) 0.000 (0.002)

Margin of victory (t� 1) �0.004 (0.002) 0.000 (0.003)

N 1254 1254 699 699

log Likelihood �570.33 �567.54 �328.74 �328.73

Pseudo R-squared 0.14 0.14 0.14 0.14

Probit estimations: coefficients are estimated marginal effects (dF/dxk), i.e., the marginal effect on Pr(y¼ 1), given a unit increase in the value of the

relevant regressor (xk), holding all other regressors at their sample means. Heteroskedasticity and serial correlation consistent standard errors are in

parentheses. Margin of victory is computed separately for each party but coefficients are shown in the same row.

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the Senate. Apart from this work, political scientistshave so far ignored its potential as a tool for causalinferences.

The RD design is best formulated in the frame-work of the Rubin Causal Model, which conceptual-izes causal inference in terms of potential outcomesunder treatment and control (Rubin, 1974, 1978,1990; Holland, 1986; Angrist and Krueger, 1999;Rosenbaum, 2002).

First, we need to introduce some notation. Let Y1ijt

denote the potential outcome for party j in district iin an election at time t if exposed to the treatmentDijt (defined more formally below) and let Y0ijt denotethe potential outcome for the same party if not exposedto the treatment. Our two outcomes of interest areSMD vote shares and PR vote shares.5

For each unit, we never observe both potentialoutcomes Y1 and Y0 but only the realized outcomeY¼DY1þ (1�D)Y0. Holland (1986) has character-ized this as the ‘‘fundamental problem of causal infer-ence.’’ For example, given that a party is the incumbentin a district, in the next election we never get toobserve the SMD and PR vote shares that it wouldattain if it was not the incumbent. It is thus impossibleto estimate causal effects for individual units (Y1� Y0).However, we can, under certain assumptions, estimatethe average treatment effect ATE¼ E[Y1� Y0] or theaverage treatment effect for the treated ATT ¼ E½Y1 �Y0jD ¼ 1� for a given population.

5 To simplify notation we do not add yet another subscript to dis-

tinguish between SMD and PR vote shares. The formulas are identi-

cal for both outcomes. We will also suppress subscripts when the

context is unambiguous.



We also need a model of the data-generatingprocess. Let LVSijt denote a party’s latent vote share.We assume that a party’s observed vote share is repre-sented by OVSijt, which is the sum of two components:

OVSijt ¼ LVSijt þ hijt ð1Þ

LVS reflects a systematic or predictable component thatis a function of the party’s attributes or actions (such asthe party program, the quality of its district candidate,campaigning efforts), and h is an exogenous, randomchance component (such as the weather on electionday) with mean zero and a continuous density. Fortractability we also assume that party j competes inelections at time t and t� 1.6

Our treatment is incumbency. As already dis-cussed, there exist two different versions of thistreatment: party incumbency and the more traditionallegislator incumbency. Following Lee (2008), we de-fine the effect of party incumbency as the causal ef-fect of being the incumbent party in a district on theSMD or PR vote share obtained in the next election.Thus, let Dijt be a binary indicator of treatment statusthat takes the value 1 if party j is the incumbent indistrict i at time t, and 0 otherwise. Note that allthat matters here is that the party’s candidate wonthe district in the last election. Such districts are con-sidered treated units, regardless of whether the in-cumbent legislator herself runs in the next election

6 This assumption is innocuous as both SPD and CSU/CDU com-

pete in all districts in every election. They also divide virtually all

district seats among themselves. Smaller parties such as the Greens

and Liberals also compete in virtually every district but normally

win all of their Bundestag seats in the PR tier.


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7 For example, unobserved candidate characteristics will not bias

our estimates because local random assignment in close districts en-

sures that they will be balanced between the treatment and control

groups.

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or not. The causal effect of legislator incumbency isdefined analogously, but here the treated group onlyconsists of those districts in which the incumbentlegislator runs. Thus, if an incumbent decides toexit, the district will be discarded from the sample.

Both measures of incumbency are characterized bysomewhat different treatment assignment mechanisms.For party incumbency, assignment to treatment is de-termined by whether the party won the plurality ofSMD votes in district i in the election at t� 1. Forlegislator incumbency, assignment to treatment isalso determined by whether the party won the pluralityof SMD votes in district i in the election at t� 1. But inaddition, the party’s candidate that won at time t� 1(the incumbent) needs to run in the next election (attime t).

To compute the margin of victory (MVijt), we rankparties in each district by their observed SMD voteshares in the election at t� 1. For the winning party,MVijt is the difference between its vote share and thevote share of the party that came second. For all otherparties in the district, MVijt is the difference betweenthe winning party’s vote share and their own voteshares. Note that by construction, MV will be positivefor winning and negative for losing parties. Thethreshold, labeled MV, is zero. Once we define MVin this way it is easy to see that the causal effect ofincumbency can be estimated with an RD design,because assignment to treatment is a deterministicfunction of whether a party’s margin of victory in theprevious election (MVt�1) exceeds 0.

The strength of the RD design stems from the factthat we know this treatment assignment mechanism.Under fairly weak smoothness assumptions (seeRubin, 1977; Hahn et al., 2000 for a rigorous discus-sion), the RD design allows us to estimate the aver-age treatment effect (ATE) at the discontinuity of thecovariate that determines treatment assignment.Even under non-random selection into treatment,the RD design yields an unbiased estimate of thetreatment effect. Why is this the case? Recall thatthe margin of victory is a function of observedvote shares. Observed vote shares in turn consistof a latent systematic component LVS that partiescan influence, but also a random component h overwhich parties cannot exert control. It can be proventhat as long as the covariate that determines assign-ment to treatment includes such a random compo-nent with a continuous density, treatment status israndomized at the threshold (Lee, 2008). Therefore,at the threshold, all observed and unobserved cova-riates will be independent of treatment assignment.



In other words, just as in a randomized experiment,treatment effects will not be confounded by omittedvariables. This provides an important advantage overcommonly used regression models which are byconstruction vulnerable to omitted variable bias.7

It is important to at least briefly consider the condi-tions under which the assumption of local random as-signment at the threshold could be wrong. Localrandom assignment critically hinges on the presenceof the random component h. This does not imply thateach district race has to be decided by this randomcomponent; in most races the random componentwill not be decisive. The key idea is that as races be-come closer and closer, confounders cease to systemat-ically affect treatment assignment. In the limit, i.e., atthe threshold, treatment assignment should be indepen-dent of all confounding variables. The plausibility ofthis assumption is a function of the degree to whichparties are able to sort around the threshold. For exam-ple, if parties had perfect control over their observedvote shares or were able to perfectly predict them,they would never run if they knew that they wouldlose. Alternatively, they would just invest enough effortto get exactly one more vote than the strongest districtopponent. Such behavior would violate our identifyingassumption. However, given the randomness inherentin elections, such a scenario seems rather implausible(Matsusaka and Palda, 1999). Just imagine the weatherhad been different on election day (Knack, 1994).

Note that in principle, all of the advantages of theRD design apply no matter whether we rely on partyor legislator incumbency as our measure of incum-bency. When estimating the causal effect of legislatorincumbency, however, strategic exit creates onepotential source of bias that even the RD designcannot fully avoid. If for incumbents that barelywon in the last election, the decision to run is notindependent of potential outcomes, our estimates ofthe causal effect of legislator incumbency will bebiased. The same is true for specifications in whichwe restrict the sample to districts in which the othermajor party did not nominate a shadow incumbent.Both the incumbent legislator’s decision to run andthe other major party’s decision to nominate a shadowincumbent are not locally randomized and thus a po-tential source of hidden bias. However, the resultspresented in Section 4 on incumbents’ decision to


oi:10.1016/j.electstud.2007.10.006

8 Results are available upon request. Higher order terms beyond the

third polynomial are generally insignificant and are thus discarded to

reduce multi-collinearity and maximize efficiency.9 Since our analysis requires lagged vote shares excluding one elec-

tion effectively means excluding two elections.

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retire suggest that strategic exit is not a significantsource of bias.

Before we proceed to estimation, a general limita-tion of the RD design needs to be mentioned. As notedabove, our ATE estimates do not identify average treat-ment effects for the entire population, but only for dis-tricts with close races. Such marginal districts may notbe representative of the whole population of districts.Unless we impose additional homogeneity assump-tions, our causal estimates will not be applicable tothe latter districts. The data are only informative abouttreatment effects for observations close to the threshold.

However, marginal districts are not uncommon inGerman elections. Over 20% of all races in an averageGerman federal election are fairly close, with thewinner in each district leading by less than 5 percent-age points. That being said, we clearly face a trade-offhere. The RD design helps us to derive credible causalestimates for the effects of incumbency, but only forclose districts. The alternative is to attempt to estimatecausal effects for the whole population by imposing as-sumptions about the treatment assignment mechanism(e.g., that parties choose districts in which they runcandidates at random, or at least that treatmentassignment is ignorable conditional on some controlvariable like past vote shares) that are almost certainlywrong. Doing so might appear to tell us somethingabout the whole population, but we will have little rea-son to be confident that it gives us the right answer. Wethink that when faced with such trade-offs, internal val-idity is more important than generalizability (Shadishet al., 2002).

5. Estimation strategy

Our model suggests the following data-generatingprocess for the observed outcomes:

Yi;j;t ¼ f�Zi;j;t�1;q

�þ h�MVi;j;t�1;d

�þDi;jbþ 3i;j ð2Þ

where f is some function according to which Zt�1, a ma-trix of district-level covariates (e.g. candidate quality,campaign effort), may affect vote shares with coeffi-cients q; h is some function that relates the margin ofvictory in each district to votes in the next election.Finally, D is our treatment indicator and b is the centralparameter of interest, identifying the causal effect ofincumbency.

At first glance, Eq. (2) is just a conventionalregression model. As already discussed earlier, thecomplication that makes the interpretation of priorresults ambiguous is the possibility that there exists



some unobserved Z that we cannot control for. SinceZ is likely to be correlated with MV, estimates ofb tend to be biased. For the RD design, in contrast,local random assignment ensures that our estimate ofb is unconfounded at the threshold, and we do notneed to control for any covariates. Just as in random-ized experiments, the inclusion of covariates shouldnot appreciably affect our estimates of b (apart fromincreasing their precision). Under the assumption thatthere is no strategic exit, this will also be true forspecifications in which we rely on legislator insteadof party incumbency.

In order to draw causal inferences from an RDdesign we need to choose the correct functional formfor h. D should only pick up the potential ‘‘jump’’ inthe conditional expectation of E½YjMVi;j;t�1� at thethreshold, and a miss-specification of the functionalform of h would lead to bias.

The common solution (Lee, 2008; Butler and Butler,2007), which we employ here as well, is to allow fora highly flexible functional form of E½YjMVi;j;t�1�. Wetherefore include a third-order polynomial in MV plusall interactions with the treatment indicator. We thus re-gress Y on MVþMV2þMV3þDþ (D�MV)þ(D�MV2)þ (D�MV3) using ordinary least squares.Since MV equals zero at the threshold, the coefficientof D identifies the ATE. The multiplicative third-or-der polynomial ensures a good fit of the functionalform of the assignment variable on both sides ofthe threshold. All our results are substantively identi-cal if we use fourth- or fifth-order polynomials in-stead.8 We compute heteroskedasticity and serialcorrelation consistent (HAC) standard errors usingBartlett kernel weights as described in Newey andWest (1987, 1994).

German federal election results were compiled byCaramani (2000). We added data on candidate char-acteristics (age, gender, and incumbency and shadowincumbency status) from Statistisches Bundesamt(various years). We originally had planned to exam-ine all Bundestag elections. But due to several wavesof redistricting we had to exclude the 1957, 1976,1980, and 2002 elections, so that we are left witheight federal elections.9 There are about 248 districts


oi:10.1016/j.electstud.2007.10.006

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per election up to 1990, and 328 districts afterunification.10

In virtually all district races, the strongest twoparties are the Social Democratic Party (SPD) andthe Christian Democratic Union/Christian SocialUnion (CDU/CSU), although third parties do obtainsome share of the vote. Accordingly, we only focuson the causal effects of incumbency for these twoparties. We cannot estimate incumbency effects forsmall parties such as the Greens and Liberals becausethese parties never win district seats.11

For both the SPD and the CDU/CSU, we estimate thecausal effects of incumbency by regressing either SMD orPR vote shares on a third-order polynomial in margin ofvictory in the previous election and all interactions withthe treatment indicator. We only show the treatment effectestimates. In each model, the causal effect of incumbencyis simply the ‘‘gap’’ in the conditional expectation of Y atthe threshold, contrasting districts that were barely wonwith districts that were barely lost in the last election bythe same party. We present specifications for three quan-tities of interest: the effect of party incumbency, the effectof legislator incumbency in general, and the effect of leg-islator incumbency in those districts in which the othermajor party did not nominate a shadow incumbent.

6. Results

6.1. Effect of incumbency on SMD vote shares

Tables 3 and 4 display the results. Concentrating onthe top halves of the tables first, we see that for allthree measures incumbency status has a substantialeffect on a party’s SMD vote share. In magnitudeand statistical significance, the effects are quite similarfor the SPD and CDU/CSU. On average, party incum-bency increases SMD vote shares in the next electionby about 1.5e1.9 percentage points.12 These effectsare significant at the 0.05 level or better.

10 Some scholars have argued that electoral dynamics in the Eastern

Lander are distinct (Jeffery and Hough, 2001; Hough and Jeffery,

2003; Falter et al., 2000). Our findings are substantively identical

if we include districts in Eastern Germany. Results are available

upon request.11 As noted earlier, even smaller parties such as the Greens and Lib-

erals compete in almost every district. Excluding the few partially

contested districts does not affect our results.12 Please note that we can rule out reverse causality, from the PR tier to

the SMD tier, due to the use of the RD design. Barely winning or losing

the PR vote in a district has no noticeable consequences in this district; it

is not associated with any district-level treatment as is the case with the

SMD vote. To put this another way, nothing changes in a district when,

say, the SPD barely wins the PR vote compared to when it barely loses it.



We find that effects on SMD vote shares are verysimilar or even slightly larger once we focus onlegislator incumbency. The exact interpretation ofthis result depends on the assumptions we are willingto make about the effects of strategic exit. If strategicexit is not very important in Germany (as the resultsin Tables 1 and 2 suggest), then the similarity of ourestimates suggests that party incumbency provides anexcellent proxy for legislator incumbency. However,if one believes strategic exit to be an issue, ourestimated legislator incumbency effect will be biasedand we should rely on the estimates for party incum-bency instead. Independent of what stance one takeson this issue, our results for the SMD tier are similarto what earlier studies of the incumbency effect inGerman elections have found (Bawn, 1999; Moserand Scheiner, 2005).

The third row of Tables 3 and 4 presents the legislatorincumbency effect for districts in which the other majorparty did not run a shadow incumbent. Here, we seesomewhat of a divergence between the results for theCDU and the SPD. For the CDU, the effect of incum-bency remains about the same and challenger qualitycan thus be ruled out as an explanation for the existenceof any incumbency advantage. For the SPD, in contrast,the size of the incumbency advantage seems to increasesomewhat, suggesting that in districts in which the CDUdoes not run a strong district candidate (as measured byshadow incumbency), SPD incumbents enjoy a largerincumbency advantage. However, this difference is notpronounced enough to be significant at conventionallevels of statistical significance.

6.2. Effect of incumbency on PR vote shares

Thus far, we have focused on the effect ofincumbency on SMD vote shares. The lower halvesof Tables 3 and 4 present tests of our core argument,displaying estimates for the average treatment effectof incumbency on PR vote shares, our measure ofspillover. To the best of our knowledge, our paper isthe first to estimate effects of incumbency on PRvote shares.

We find that for both parties, incumbency statushas a positive and substantial effect on PR vote shares.This is true for all three measures of incumbency. Onaverage, party incumbency increases PR vote sharesby about 1.7 percentage points for the SPD and byabout 1.4 percentage points for the CDU. These esti-mates are significant at the 0.05 level or better. Forboth parties, the legislator incumbency effect estimateis almost identical to the party incumbency effect


oi:10.1016/j.electstud.2007.10.006

Table 3

SPD: causal effect of incumbency on SMD and PR vote shares

Incumbent Non-incumbent ATE 0.90 CI N

LB UB

Effect on SMD vote shares

Party incumbency 46.45 (0.51) 44.95 (0.49) 1.51 (0.59) 0.54 2.47 1958

Legislator incumbency 46.03 (0.59) 44.41 (0.50) 1.61 (0.66) 0.52 2.7 1514

Legislator incumbency

(no shadow incumbent)

46.78 (0.81) 44.41 (0.51) 2.36 (0.89) 0.90 3.82 1236

Effect on PR vote shares





43.63 (0.84) 41.49 (0.56) 2.14 (0.90) 0.66 3.62 1236

Regression coefficients with heteroskedasticity and serial correlation consistent standard errors are in parentheses. ATE represents the average treat-

ment effect, i.e., the effect of incumbency on SMD and PR vote shares at the threshold. All estimates are based on a multiplicative third-order poly-

nomial fit of the assignment variable and the treatment indicator to both sides of the threshold (only the treatment effect estimates are shown). LB

and UB mark the endpoints of 0.90 confidence intervals.

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estimate. When we focus on districts in which theother major party does not run a shadow incumbent,we again see somewhat of a divergence between theresults for the CDU and the SPD. For the CDU, theeffect size stays about the same, and challenger qual-ity can thus be ruled out as an explanation for the ex-istence of spillover. For the SPD, in contrast, theeffect size increases somewhat, suggesting that in dis-tricts without a strong CDU challenger, SPD incum-bents are particularly successful in boosting theirparty’s PR vote share. As for SMD votes, this differ-ence is noteworthy but not significant at conventionallevels of statistical significance.

Fig. 1 provides a graphical representation of theseresults for the SPD. The upper (lower) graph displaysthe effect of party (legislator) incumbency.13 In thesegraphs, the vertical axis displays the SPD’s vote sharein each district at time t, with the left (right) graphshowing SMD (PR) vote shares. The horizontal axisdisplays the margin of victory at time t� 1, with thedashed vertical line at zero marking the threshold.All observations to the right (left) of the dashed linerepresent treated districts (control districts). The curvesplot the fitted values from our polynomial fit on bothsides of the threshold. Each data point represents a localaverage of the outcome variable (SMD or PR voteshares) for intervals of margin of victory with a widthof 0.05.

Several features are apparent. First, note that thereexists a positive relationship between margin of victory

13 Figures for shadow incumbency and the CDU look almost iden-

tical and are omitted here to economize on space. They are available

upon request.



and vote shares in both the SMD and PR tier. If a partywins (loses) by a larger margin in the last district race,it is more likely to receive a higher (lower) vote sharein the next race. Second, and more importantly, we finda noticeable discontinuity at each of the four thresh-olds, graphically representing the average causal effectof party and legislator incumbencies on SMD and PRvote shares. If incumbency had no causal effect, therewould be no such discontinuity. Also note that we donot see any discontinuous ‘‘jumps’’ in the conditionalexpectation functions except at the thresholds; the rela-tionships between margin of victory and our outcomevariables are generally smooth and well-approximatedby a multiplicative polynomial fit.

Taken together, these findings lend strong support toour claim that incumbents not only enjoy an incum-bency advantage, but also attract additional PR votesfor their parties in their districts. Note that for partyincumbency (and to a lesser extent for legislatorincumbency), these treatment effect estimates arecausal estimates based on very weak assumptions. Itseems highly unlikely that these differences in voteshares are attributable to some unobserved confounder.

How do our estimates compare to earlier results onspillover effects in mixed electoral systems? Recallthat so far the spillover literature has focused onthe presence of district candidates, not incumbency.Ferrara et al. (2005: 44) find evidence for spillovereffects for three small parties in the 1953 Bundestagelection, but do not provide any point estimates. Asnoted earlier, Cox and Schoppa cannot estimate theeffect of running SMD candidates in German elec-tions because of lack of variation in their independentvariable.


oi:10.1016/j.electstud.2007.10.006

Table 4

CDU: causal effect of incumbency on SMD and PR vote shares

Incumbent Non-incumbent ATE 0.90 CI N

LB UB

Effect on SMD vote shares





43.47 (0.68) 41.48 (0.69) 1.99 (0.85) 0.60 3.39 1021

Effect on PR vote shares





40.12 (0.67) 38.71 (0.69) 1.40 (0.85) 0.01 2.8 1021

Regression coefficients with heteroskedasticity and serial correlation consistent standard errors are in parentheses. ATE represents the average treat-

ment effect, i.e., the effect of incumbency on SMD and PR vote shares at the threshold. All estimates are based on a multiplicative third-order poly-

nomial fit of the assignment variable and the treatment indicator to both sides of the threshold (only the treatment effect estimates are shown). LB

and UB mark the endpoints of 0.90 confidence intervals.

14 Details can be found in the supplementary material for this paper,

available on the authors’ websites, which also contains additional ro-

bustness and balance tests.

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Ferrara et al. (2005) also present estimates for theeffect of running district candidates in other countries.Point estimates range from approximately 0 to 5 per-centage points of vote share, depending on the partythey look at. Herron and Nishkawa (2001) find evenlarger effects for several Japanese parties. The averagetreatment effects that we find here are considerablysmaller. It might be the case, of course, that incum-bency is just not as important a source of spillover asthe presence of district candidates, or that its effectvaries from country to country. While we cannot settlethis question one way or the other in this paper, wethink that it is quite possible that prior estimates are bi-ased due to self-selection. If parties tend to run districtcandidates in districts in which they expect to do betterthan average, the spillover effects found in earlier workwill be biased upwards.

6.3. Effect of incumbency on PR vote sharesof other parties

So far, our results demonstrate that incumbents doindeed attract additional PR votes in their districts. Itwould be interesting, of course, to see who loses thesevotes. In order to examine this question, we re-ran ourmodels, replacing the outcome variable by the PR voteshare of each of the other parties. Results are shown inTable 5.

We find that most of the PR votes that incumbentsare able to attract for their parties come from the othermajor party. On average, in their districts SPD incum-bents reduce the PR vote share of the CDU by about1.5 percentage points. CDU incumbents cause a compa-rable loss for the SPD of about 1.4 percentage points.



We cannot reject the null hypotheses that for boththe CDU and the SPD, incumbency has no effect onthe PR vote shares of the two smaller parties (Liberalsand Greens). Incumbency predominantly leads to shiftsin PR vote shares from one of the major parties to theother. The reason is probably quite straightforward: theother major party has many more voters to lose to be-gin with than the small parties. Even if all parties lostan equal percentage of their voters to the incumbentparty, a switch of 2 or 3% of CDU voters to the SPDwould be much more noticeable than the switch of 2or 3% of Green or FDP voters. In our statistical model,switches due to spillover are large enough for the ma-jor parties to register as statistically significant,whereas for the FDP and Greens, the noise overwhelmsthe spare information that is in the data.

6.4. Substantive magnitude of spillover:simulation results

One final question remains: are spillover effects largeenough to actually trigger shifts in Bundestag majori-ties? In order to assess the substantive importance ofspillover caused by incumbency, we wrote a numericalsimulation of the distribution of Bundestag seats inthe absence of spillover.14

We find that spillover generally leads to net shifts of10e15 Bundestag seats. It tends to have the strongestimpact on the Bundestag seat distribution whenevera disproportionate share of district seats was won by


oi:10.1016/j.electstud.2007.10.006

Fig. 1. SPD: causal effect of incumbency on SMD and PR vote shares.

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one of the major parties in the previous election. The ef-fects of such landslides are still felt in the next electionwhen incumbents are able to attract additional PR votesfor their parties. Overall, shifts in the Bundestag seatdistribution caused by spillover are often large enoughto alter the composition of the Bundestag in importantways. As expected, smaller parties are largely unaf-fected by spillover since they are never district incum-bents; the SPD gains somewhat more from theexistence of spillover than the CDU/CSU.



As an illustration, we show simulation results forthe 2002 Bundestag election, which pitted ChancellorGerhard Schroder (SPD) and the SPD/Greens coalitionagainst challenger Edmund Stoiber, who was thecandidate of a potential CDU/CSU/Liberals coalition.The original election results are displayed in the firstrow of Table 6. The SPD/Greens coalition won theelection by a narrow margin, gaining 306 out of 603seats. CDU/CSU and Liberals captured 295 seats,missing a Bundestag majority by only seven seats.


oi:10.1016/j.electstud.2007.10.006

Table 5

Causal effect of SPD and CDU incumbency on PR vote shares of other parties

Effect of SPD incumbency

SPD incumbent SPD not incumbent ATE UB LB

CDU PR vote share 38.71 (0.7) 40.24 (0.66) �1.53 (0.84) �2.91 �0.15

Greens PR vote share 7.5 (0.5) 6.96 (0.49) 0.54 (0.59) �0.43 1.51

FDP PR vote share 9.21 (0.43) 9.01 (0.44) 0.20 (0.53) �0.67 1.07

Effect of CDU incumbency

CDU incumbent CDU not incumbent ATE UB LB

SPD PR vote share 41.66 (0.57) 43.08 (0.63) �1.42 (0.74) �2.64 �0.19

Greens PR vote share 6.96 (0.49) 7.50 (0.50) �0.54 (0.59) �1.51 0.43

FDP PR vote share 9.17 (0.47) 9.17 (0.43) 0.01 (0.57) �0.93 0.94

Regression coefficients with heteroskedasticity and serial correlation consistent standard errors are in parentheses. ATE represents the average

treatment effect, i.e., the effect of incumbency on SMD and PR vote shares at the threshold. All estimates are based on multiplicative third-order

polynomial fit of the assignment variable and the treatment indicator to both sides of the threshold (only the treatment effect estimates are shown).

LB and UB mark the endpoints of 0.90 confidence interval.

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The second and third rows of Table 6 display thecounterfactual Bundestag seat distribution withoutspillover. If there had been no spillover due to incum-bency, either of the coalitions could have won the 2002election. If we assume that spillover effects were rela-tively large (the upper bound of the 0.90 confidence in-terval for our treatment effect estimate), the CDU/CSUtogether with the Liberals would have gained a stablemajority of 304 seats, enabling them to form a coalitiongovernment. Fig. 2 displays the distribution of simu-lated Bundestag seats for the CDU/CSU/FDP coalition.Overall, we find that in 20% of our simulations of the2002 Bundestag election, a CDU/CSU/FDP coalitionwould have won the majority of seats in the absenceof spillover effects caused by incumbency.

7. Conclusion

In this paper, we have identified incumbency asanother source of spillover in mixed electoral systems.Using two different measures of incumbency, we foundthat incumbency has a sizeable, positive effect on PRvote shares in Germany’s mixed electoral system. Wehave also shown that such spillover effects are potentenough to alter election outcomes. According to our

Table 6

The effect of spillover on the seat distribution in the 2002 Bundestag

Party CDU/CSU FDP SPD Greens PD

Seats with spillover (original results)248 47 251 55 2

Seats without spillover (counterfactual)

0.90 LB 245 49 254 57 2

0.90 UB 254 50 244 57 2

Total denotes the total number of seats including Uberhangmandate. Majorit

of the Bundestag.



simulation results, for example, spillover effects possi-bly lead to the close victory of the SPD/Green coalitionin the 2002 Bundestag election. In contrast to the priorliterature on spillover, the causal inferences we havedrawn using a quasi-experimental regression-disconti-nuity design are not vulnerable to omitted variablebias.

Research on voting behavior in mixed electoralsystems has almost exclusively focused on the PRtier so far. The existence of substantial spillover effectsstrongly suggests that district-level factors are moreimportant for national election outcomes than has pre-viously been thought. Regarding the causal mecha-nisms underlying spillover, our paper shows thatspillover is not caused by strategic exit. The evidenceis more ambiguous regarding challenger quality. Forthe SPD, we presented some preliminary evidencethat weaker challengers cause incumbents to performbetter. We were not able to find any such effect for theCDU, however. This difference in the impact of challengerquality merits further research, as do other potential causalmechanisms such as district service. It is also worth askingto what extent our findings are generalizable. While wehave only looked at German federal elections in this paper,we expect incumbency to also be a source of spillover in

S Total Majority CDU/FDP SPD/Greens

603 302 295 306

605 303 294 311

604 303 304 300

y denotes the minimum number of seats necessary for majority control


oi:10.1016/j.electstud.2007.10.006

290 295 300 305

0.00

0.05

0.10

0.15

0.20

Seats for CDU/CSU/FDP Coaliton

Den

sity

Bundestag Majority

Fig. 2. Seat allocation in the 2002 Bundestag in a simulated counter-

factual world without spillover. The curve represents the probability

density of the estimated number of seats for the CDU/CSU/FDP co-

alition (based on 1000 simulated sets of parameters drawn from their

sampling distribution in the baseline model presented in Table 3. See

supplementary material for details).

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other electoral systems. Extending the scope of inquiry toother countries is a logical next step.

Finally, the regression-discontinuity design we haveused here has much wider applicability. It is a powerfultool for causal inference that should be used more fre-quently in research on comparative political behavior.

Appendix A. Supplementary data

Supplementary data associated with this article canbe found, in the online version, at 10.1016/j.electstud.2007.10.006.

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